3 Preview of Grade 7 AF Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations, or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).CaliforniaStandards

5 Symbol Meaning Word PhrasesAn inequality is a statement that compares two expressions by using one of the following symbols: <, >, ≤, ≥, or .SymbolMeaningWord Phrases<>≤≥is less thanFewer than, belowis greater thanMore than, aboveis less than or equal toAt most, no more thanis greater than or equal toAt least, no less than

6 An inequality that contains a variable is an algebraic inequalityAn inequality that contains a variable is an algebraic inequality. A value of the variable that makes the inequality true is a solution of the inequality.An inequality may have more than one solution. Together, all of the solutions are called the solution set.You can graph the solutions of an inequality on a number line. If the variable is “greater than” or “less than” a number, then that number is indicated with an open circle.

7 x is either greater than 3 or less than–1. A compound inequality is the result of combining two inequalities. The words and and or are used to describe how the two parts are related.x > 3 or x < –1–2 < y and y < 4x is either greater than 3 or less than–1.y is both greater than –2 and less than y is between –2 and 4.The compound inequality –2 < y and y < 4 can be written as –2 < y < 4.Writing Math

8 a > 5 b ≤ 3 This open circle shows that 5 is not a solution.If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle.This closed circle shows that 3 is a solution.b ≤ 3

9 Additional Example 1: Writing InequalitiesWrite an inequality for each situation.A. There are at least 15 people in the waiting room.“At least” means greaterthan or equal to.number of people ≥ 15B. The tram attendant will allow no morethan 60 people on the tram.“No more than” meansless than or equal to.number of people ≤ 60

10 Additional Example 2: Graphing Simple InequalitiesGraph each inequality.Draw an open circle at 3. The solutions are values of n less than 3, so shade to the left of 3.A. n < 3–3 –2 –B. a ≥ –4Draw a closed circleat –4. The solutions are –4 and values of a greater than –4, so shade to the right of –4.–6 –4 –

12 Check It Out! Example 1Write an inequality for each situation.A. There are at most 10 gallons of gas in the tank.“At most” means lessthan or equal to.gallons of gas ≤ 10B. There is at least 10 yards of fabric left.“At least” meansgreater than or equal to.yards of fabric ≥ 10

13 Check It Out! Example 2 Graph each inequality.Draw a closed circle at 2. The solutions are 2 and values of p less than 2, so shade to the left of 2.A. p ≤ 2–3 –2 –B. e > –2Draw an open circleat –2. The solutions are values of e greater than –2, so shade to the right of –2.–3 –2 –

14 Lesson Quiz: Part IWrite an inequality for each situation.1. No more than 220 people are in the theater.2. There are at least a dozen eggs left.3. Fewer than 14 people attended the meeting.people in the theater ≤ 220number of eggs ≥ 12people attending the meeting < 14